Three types of surfaces in the Schroeder–Webster (SW) theory, i.e., sliding, mixed, and sticking surfaces, have been verified via finite element analysis of an axisymmetric compression test for a metallic specimen. Judging from (i) the radial profile of the pressure at the top elements and (ii) the radial displacement at the top nodes, the three types of SW surfaces are not manifested in the numerical simulation. However, the SW friction compensation model developed for the SW-sliding surface is remarkably reliable in predicting the measured stress–strain curve of the barreled specimen down to the height-to-diameter ratio of 0.1. The origin of this reliability is discussed along with recommendations for using the SW friction compensation model for the SW-sliding surface.

References

References
1.
Voce
,
E.
,
1948
, “
The Relationship Between Stress and Strain for Homogeneous Deformation
,”
J. Inst. Metals
,
74
, pp.
537
562
.
2.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1983
, “
A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures
,”
Proceedings of the 7th International Symposium on Ballistics, Organizing Committee of the 7th ISB
,
Hague
,
Apr. 19–21
, pp.
541
547
.
3.
Shin
,
H.
, and
Kim
,
J.-B.
,
2010
, “
A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes
,”
ASME J. Eng. Mater. Technol.
,
132
(
2
), p.
021009
.
4.
Nakamura
,
T.
,
Tanaka
,
S.
,
Hayakawa
,
K.
, and
Fukai
,
Y.
,
2000
, “
A Study of the Lubrication Behavior of Solid Lubricants in the Upsetting Process
,”
ASME J. Tribol.
,
122
(
4
), pp.
803
808
.
5.
Azushima
,
A.
,
2000
, “
FEM Analysis of Hydrostatic Pressure Generated Within Lubricant Entrapped Into Pocket on Workpiece Surface in Upsetting Process
,”
ASME J. Tribol.
,
122
(
4
), pp.
822
827
.
6.
Azushima
,
A.
,
Yanagida
,
A.
, and
Tani
,
S.
,
2010
, “
Permeation of Lubricant Trapped Within Pocket Into Real Contact Area on the End Surface of Cylinder
,”
ASME J. Tribol.
,
133
(
1
), p.
011501
.
7.
Mizuno
,
T.
, and
Hasegawa
,
K.
,
1982
, “
Effects of Die Surface Roughness on Lubricating Conditions in the Sheet Metal Compression-Friction Test
,”
ASME J. Lubr. Technol.
,
104
(
1
), pp.
23
28
.
8.
Ramaraj
,
T. C.
, and
Shaw
,
M. C.
,
1985
, “
A New Method of Evaluating Metal-Working Lubricants
,”
ASME J. Tribol.
,
107
(
2
), pp.
216
219
.
9.
Krishna
,
C. H.
,
Davidson
,
M. J.
,
Nagaraju
,
C.
, and
Kumar
,
P. R.
,
2015
, “
Effect of Lubrication in Cold Upsetting Using Experimental and Finite Element Modeling
,”
J. Test. Eval.
,
43
(
1
), pp.
53
61
.
10.
Misirili
,
C.
,
2014
, “
On Materials Flow Using Different Lubricants in Upsetting Process
,”
Ind. Lub. Tribol.
,
66
(
5
), pp.
623
631
.
11.
Banerjee
,
J. K.
,
1985
, “
Barreling of Solid Cylinders Under Axial Compression
,”
ASME J. Eng. Mater. Technol.
,
107
(
2
), pp.
138
144
.
12.
Banerjee
,
J. K.
, and
Cárdenas
,
G.
,
1985
, “
Numerical Analysis on the Barreling of Solid Cylinders Under Axisymmetric Compression
,”
ASME J. Eng. Mater. Technol.
,
107
(
2
), pp.
145
147
.
13.
Lee
,
J.-H.
,
Shin
,
H.
,
Kim
,
J.-B.
,
Kim
,
J.-Y.
,
Park
,
S.-T.
,
Kim
,
G.-L.
, and
Yoon
,
T.-S.
,
2019
, “
Determination of the Flow Stress–Strain Curve of Aluminum Alloy and Tantalum Using Compressive Load–Displacement Curves of a Hat-Type Specimen
,”
ASME J. Appl. Mech.
,
86
(
3
), p.
031012
.
14.
Lee
,
C. H.
, and
Altan
,
T.
,
1972
, “
Influence of Flow Stress and Friction Upon Metal Flow in Upset Forging of Rings and Cylinders
,”
J. Eng. Ind.
,
94
(
3
), pp.
775
782
.
15.
Kim
,
S.-H.
,
Kim
,
M.-K.
,
Shin
,
H.
, and
Lee
,
K. Y.
,
2018
, “
Measurement of a Nearly Friction-Free Stress–Strain Curve of Silicone Rubber up to a Large Strain in Compression Testing
,”
Exp. Mech.
,
58
(
9
), pp.
1479
1484
.
16.
Tan
,
X.
,
2011
, “
Evaluation of Friction in Upsetting
,”
Prod. Eng. Res. Dev.
,
5
(
2
), pp.
141
149
.
17.
Lee
,
J.-H.
,
Shin
,
H.
,
Seo
,
S.-J.
,
Lee
,
J.-G.
,
Lee
,
J.-O.
,
Yoon
,
T.-S.
, and
Jeong
,
C.-S.
,
2019
, “
A Design of a Phenomenological Friction-Compensation Model via Numerical Experiment for the Compressive Flow Stress–Strain Curve of Copper (in Korean)
,”
Kor. J. Comput. Design Eng.
,
24
(
1
), pp.
1
9
.
18.
Shin
,
H.
, and
Kim
,
J.-B.
,
2019
, “
Evolution of Specimen Strain Rate in Split Hopkinson Bar Test
,”
Proc. Inst. Mech. Eng. C
,
233
(
13
), pp.
4667
4687
.
19.
Couque
,
H.
,
2014
, “
The Use of the Direct Impact Hopkinson Pressure Bar Technique to Describe Thermally Activated and Viscous Regimes of Metallic Materials
,”
Philos. Trans. R. Soc. A
,
372
, p.
20130218
.
20.
Frutschy
,
K. J.
, and
Clifton
,
R. J.
,
1998
, “
High-Temperature Pressure-Shear Plate Impact Experiments on OFHC Copper
,”
J. Mech. Phys. Sol.
,
46
(
10
), pp.
1723
1743
.
21.
Schroeder
,
W.
, and
Webster
,
D. A.
,
1949
, “
Press-Forging Thin Sections: Effect of Friction, Area, and Thickness on Pressure Required
,”
ASME J. Appl. Mech.
,
16
, pp.
289
294
.
22.
Siebel
,
E.
,
1923
, “
Grundlagen zur Berechnung des Kraft- und Arbeitsbedarfs Beim Schmieden und Walzen (Basics for Calculating the Force and Work Requirements of Forging and Rolling)
,”
Stahl. Und. Eisen
,
43
(
41
), pp.
1295
1298
.
23.
Siebel
,
E.
, and
Pomp
,
A.
,
1927
, “
Die Ermittlung der Formänderungsfestigkeit von Metallen Durch den Stauchversuch (Determination of the Deformation Strength of Metals by the Compression Test)
,”
Mitt. Kaiser. Wilhelm. Inst. Eisenforsch
,
9
(
8
), pp.
157
171
.
24.
Han
,
H.
,
2002
, “
The Validity of Mechanical Models Evaluated by Two-Specimen Method Under the Known Coefficient of Friction and Flow Stress
,”
J. Mater. Process. Technol.
,
122
(
2–3
), pp.
386
396
.
25.
Loizou
,
N.
, and
Sims
,
R. B.
,
1953
, “
The Yield Stress of Pure Lead in Compression
,”
J. Mech. Phys. Solids
,
1
(
4
), pp.
234
243
.
26.
Richardson
,
G. R.
,
Hawkins
,
D. N.
, and
Sellars
,
C. M.
,
1985
,
Worked Examples in Metal Working
,
Institute of Metals
,
London
.
27.
Thompsen
,
E. G.
,
Yang
,
C. T.
, and
Kobayashi
,
S.
,
1965
,
Mechanics of Plastic Deformation in Metal Processing
,
Macmillan
,
New York
.
28.
Christiansen
,
P.
,
Martins
,
P. A. F.
, and
Bay
,
N.
,
2016
, “
Friction Compensation in the Upsetting of Cylindrical Test Specimens
,”
Exp. Mech.
,
56
(
7
), pp.
1271
1279
.
29.
Smith
,
K. K.
, and
Kassner
,
M. E.
,
2016
, “
Through-Thickness Compression Testing of Commercially Pure (Grade II) Titanium Thin Sheet to Large Strains
,”
J. Metall.
,
2016
, p.
6178790
.
30.
Altinbalik
,
T.
,
Akata
,
H.
, and
Can
,
Y.
,
2007
, “
An Approach for Calculation of Press Loads in Closed-Die Upsetting of Gear Blanks of Gear Pumps
,”
Mater. Des.
,
28
(
2
), pp.
730
734
.
31.
Hill
,
R.
,
1950
,
The Mathematical Theory of Plasticity
,
Oxford University Press
,
London
, pp.
262
281
.
32.
Rand
,
J. L.
,
1967
,
An Analysis of the Split Hopkinson Pressure Bar
, Technical Report (NOLTR 67-156),
US Naval Ordnance Laboratory
,
Silver Spring, MD
.
33.
Cook
,
M.
, and
Larke
,
E. C.
,
1945
, “
Resistance of Copper and Copper Alloys to Homogeneous Deformation in Compression
,”
J. Inst. Metals
,
71
(
12
), pp.
371
390
.
34.
Avitzur
,
B.
,
1968
,
Metal Forming: Processes and Analysis
,
McGraw-Hill
,
New York
.
35.
Schey
,
J. A.
,
Venner
,
T. R.
, and
Takomana
,
S. L.
,
1982
, “
The Effect of Friction on Pressure in Upsetting at Low Diameter-to-Height Ratios
,”
J. Mech. Work. Technol.
,
6
(
1
), pp.
23
33
.
36.
Hartley
,
P.
,
Sturgess
,
C. E. N.
, and
Rowe
,
G. W.
,
1980
, “
Influence of Friction on the Prediction of Forces, Pressure Distributions and Properties in Upset Forging
,”
Int. J. Mech. Sci.
,
22
(
12
), pp.
743
753
.
37.
Bugini
,
A.
,
Maccarini
,
G.
,
Giardini
,
C.
,
Pacagnella
,
R.
, and
Levi
,
R.
,
1993
, “
The Evaluation of Flow Stress and Friction in Upsetting of Rings and Cylinders
,”
CIRP Ann.
,
42
(
1
), pp.
335
338
.
38.
Tan
,
X.
,
Zhang
,
W.
, and
Bay
,
N.
,
1999
, “
A New Friction Test Using Simple Upsetting and Flow Analysis
,”
Adv. Technol. Plast.
,
1
(
6
), pp.
365
370
.
39.
Kamler
,
F.
,
Niessen
,
P.
, and
Pick
,
R. J.
,
1995
, “
Measurement of the Behaviour of High Purity Copper at Very High Rates of Straining
,”
Canad. J. Phys.
,
73
(
5–6
), pp.
295
303
.
40.
Bertholf
,
L. D.
, and
Karnes
,
C. H.
,
1975
, “
Two-Dimensional Analysis of the Split Hopkinson Pressure Bar System
,”
J. Mech. Phys. Solids
,
23
(
1
), pp.
1
19
.
41.
Cha
,
S. H.
,
Shin
,
H.
, and
Kim
,
J. B.
,
2010
, “
Numerical Investigation of Frictional Effects and Compensation of Frictional Effects in Split Hopkinson Pressure Bar (SHPB) Test (in Korean)
,”
Trans. Korean Soc. Mech. Eng. A.
,
34
(
5
), pp.
511
518
.
42.
Gorham
,
D. A.
,
Pope
,
P. H.
, and
Cox
,
O.
,
1984
, “
Sources of Error in Very High Strain Rate Compression Tests
,”
Inst. Phys. Conf. Ser.
,
1984
(
70
), pp.
151
158
.
43.
Hall
,
I. W.
, and
Guden
,
M.
,
2003
, “
Split Hopkinson Pressure Bar Compression Testing of an Aluminum Alloy: Effect of Lubricant Type
,”
J. Mater. Sci.
,
22
(
21
), pp.
1533
1535
.
44.
Mori
,
L. F.
,
Krishnan
,
N.
,
Cao
,
J.
, and
Espinosa
,
H. D.
,
2007
, “
Study of the Size Effects and Friction Conditions in Microextrusion—Part II: Size Effect in Dynamic Friction for Brass-Steel Pairs
,”
ASME J. Manuf. Sci. Eng.
,
129
(
4
), pp.
677
689
.
45.
Wang
,
Z. J.
, and
Cheng
,
L. D.
,
2009
, “
Experimental Research and Numerical Simulation of Dynamic Cylinder Upsetting
,”
Mater. Sci. Eng.
,
499
(
1–2
), pp.
138
141
.
46.
Jankowiak
,
T.
,
Rusinek
,
A.
, and
Lodygowski
,
T.
,
2011
, “
Validation of the Klepaczko–Malinowski Model for Friction Correction and Recommendations on Split Hopkinson Pressure Bar
,”
Finite Elem. Anal. Des.
,
47
(
10
), pp.
1191
1208
.
47.
Lu
,
Y.
, and
Zhang
,
S.
,
2013
, “
Study on Interface Friction Model for Engineering Materials Testing in Split Hopkinson Pressure Bar Tests
,”
Mod. Mech. Eng.
,
3
(
1
), pp.
27
33
.
48.
Siviour
,
C. R.
, and
Walley
,
S. M.
,
2018
, “
Inertial and Frictional Effects in Dynamic Compression Testing
,”
The Kosky-Hopkinson Bar Machine
,
Springer
,
New York
, pp.
205
247
.
49.
Shin
H.
, and
Kim
,
J.-B.
,
2012
, “
Description Capability of a Simple Phenomenological Model for Flow Stress of Copper in an Extended Strain Rate Regime
,”
Proceedings of the 4th International Conference on Design and Analysis of Protective Structures
,
Jeju, Korea
,
June 19–22
, Paper No. T8-10, pp.
1
6
.
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